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Synthetic biology is increasingly used to develop sophisticated living devices for basic and applied research. Many of these genetic devices are engineered using multi-copy plasmids, but as the field progresses from proof-of-principle demonstrations to practical applications, it is important to develop single-copy synthetic modules that minimize consumption of cellular resources and can be stably maintained as genomic integrants. Here we use empirical design, mathematical modeling, and iterative construction and testing to build single-copy, bistable toggle switches with improved performance and reduced metabolic load that can be stably integrated into the host genome. Deterministic and stochastic models led us to focus on basal transcription to optimize circuit performance and helped to explain the resulting circuit robustness across a large range of component expression levels. The design parameters developed here provide important guidance for future efforts to convert functional multi-copy gene circuits into optimized single-copy circuits for practical, real-world use.